Background

This seems a topic that keeps showing up again and again. After
every MF#K Meetup last Tuesday of every month we always go out for a
couple of beers and speak heavily in favor of the language that we like the
most. There are people who seem to need types to code, I will include myself
in this group, while others seem to do fine with languages without types as
for example Clojure, Erlang, Elixir, … My former
workmate, Brandon Lucas, keeps trolling on how you can’t model a
state-machine with types, and until I wrote this post, I would totally agree.

What you normally see in blog post when this topic is explained is something
similar to this (I will draw some ASCII art to give a better understanding):

What is represented here is a state machine for a light switch. The state is
defined as a sum type (algebraic data type) of the two values it can be. But,
then when you need to perform the state transition, you would see how people
fallback to a function to handle this logic.

In my example, I have deliberately introduced a bug in the
transition function just to prove why this approach is problematic.

This is one of the misconceptions that you hear people talking about when they make
the transition to functional programming languages. They think just because
they have modeled the domain with a few sum and product types (algebraic data
types) it’s all good and you can then claim absolute sentences
like: “Make illegal states unrepresentable”
and “Making Impossible States Impossible” and therefore you probably
don’t need to test that part of the code, which is obviously a wrong
misconception of what the authors tries to point out.

We need to be very thoughtful (and mostly careful) when we make those kind of
statements, specially due to the audiences that might receive (conceive) these
messages.

Not accessible Sum Type Case Constructors: By hiding the underlying case
constructors for a given sum type, you can ensure that only specific parts of
the code can instantiate your type. Example: type FooBar = private | Foo
of int | Bar of float

We combine the concepts 1. and 3. to define the State type, which we limit to
only two states: TurnedOn and TurnedOff, which also requires to introduce
two type terms: On and Off.

Finally, we just need to expand our domain with the transition types, which we
can use concept 2. to create two transition states: TurnOn and TurnOff,
which will subsequently require to have the opposite state as input parameter.

That’s it. Now our domain model contains all the logic while our functions just
are pure interfaces with no logic whatsoever, see both helper functions, for the
initXXX and turnXXX functions. The functions just return the internal State
type, which gets tagged by the type definitions. Pretty nifty right?

And we can be sure that no invalid State is created because we ensured that it
can’t be instantiated from outside the module (and sub modules). So even though
type 'a Switch is a generic type, we have limited only to the two
states mentioned before.

The only minor issue is that type abbreviation (alias) in F# are erased at
compile time and therefore not available at runtime,
as Marcus Griep points out in the following tweet,
therefore it’s a bit more difficult to output the currently state (see in next
coding blocks how this can be overcome).

Demo:

openLightleton=Switch.initOff|>Switch.turnOnletoff=on|>Switch.turnOffleterror=off//|>Switch.turnOff(* error FS0001: Type mismatch. Expecting a
TurnedOff -> 'a
but given a
TurnOff
The type 'Off' does not match the type 'On' *)//on=off(* error FS0001: Type mismatch. Expecting a
TurnedOn
but given a
TurnedOff
The type 'On' does not match the type 'Off' *)on|>Output.stateoff|>Output.state

A bit more complex example where we just want to automate the switch to turn
on/off a couple of times in a row. To be able to do this, we introduce the
Either sum type for better readability, but the built-in
Choice<'a,'b>F# type could be used as well. This construct will
also allow us to make a better output printer than the one that is based on
.NET Reflection as we have a guarantee of which types go in to the Left and
Right wrappers.

>
module Util = begin
type ('a,'b) Either =
| Right of 'a
| Left of 'b
end
>
val blinking :
_arg1:(TurnedOn,TurnedOff) Either -> (TurnedOn,TurnedOff) Either
>
val sprint : _arg1:(TurnedOn,TurnedOff) Either -> string
>
val foldHelper :
_arg1:(TurnedOn,TurnedOff) Either list ->
('a -> (TurnedOn,TurnedOff) Either list)
> on off on off on off on off on off on off on off on off val it : unit = ()

Conclusion:

I hope I can convince others that it is possible to model a state machine
exclusively by using the type system, while keeping the logic out of the
function layer. It uses a few type tricks that are present in F# but probably
also in other ML alike languages.

Note: Don’t forget to ALWAYS use FsCheck, F# implementation of Haskells
QuickCheck, even if you use this kind of approach. We are all human and
therefore can fail. If you just remember this last part, You would make me a
happy person.